# Investigations Blog

## Who Gets Challenged to Extend Their Thinking? A Conversation About Differentiation

In conversations about differentiation, strategies to scaffold learning for students who need more support, and strategies to extend the learning for students who are ready for more challenge often come up. One topic that is rarely considered however, is the importance of finding ways to offer students who typically need more support, opportunities to think about a task in ways that will extend their thinking about the mathematics. In the following conversation, excerpted from the Supporting...

read more## Are There Going to Be More Than 20? More Than 50?

Many of us were taught to “estimate” in elementary school. Maybe we were asked how many jellybeans there were in a jar. Or asked to round before finding the answer to a computation problem. But for many of us there was little connection between those activities and actually solving problems. I would argue that estimating — determining what an approximate and reasonable answer might be — should be a part of the process of solving problems. A visit I made to a 1st grade classroom at the end of...

read more## “Why are there so much 1s in these numbers?”

Last spring, I visited a Kindergarten classroom near the end of the year. Students were participating in a Math Workshop focused on the teen numbers, choosing among activities that asked them to identify and recognize teen numbers; to represent them in several different ways (e.g. on Ten Frames, with cubes, with numerals); and, ultimately, to come to see them as being composed of ten ones and some numbers of ones. I wandered over to Stella, who was playing Race to the Top: Teen Numbers. In...

read more## Reflections on NCSM/NCTM, Part 2

Six of our staff traveled to San Diego to attend the NCSM and NCTM conferences at the beginning of April. Below are four staff members’ reflections on a session that stood out to them. (Read the first three here.) Keith: “The Iris Carl Equity Address: Equity and Agency from Inside the Classroom” by José Luis Vilson (NCTM) José Vilson began his talk with an elegant, powerful statement — “Equity is belonging.” — and then challenged us with this question: “Do you believe your students belong?”...

read more## Reflections on NCSM/NCTM, Part 1

Six of our staff traveled to San Diego to attend the NCSM and NCTM conferences at the beginning of April. Below are three staff members’ reflections on a session that stood out to them. Four more to follow next time. Keith: “From Oakland to Wakanda: Transforming Mathematics Classrooms to Become Empowering Spaces” by Imani Masters Goffney (NCTM) Imani Masters Goffney gave a fascinating talk about making math classrooms equitable spaces for learning. She used the movie Black Panther as a context...

read more## A Conversation about “Key Words”

In my years of leading in-person and online professional development, the idea of teaching students that certain “key words” signify a particular operation (e.g. “altogether means add”) often comes up when discussing story problems. People also generally see the power of the story problem routine that Investigations uses to support students in making sense of and solving story problems. This led me to start a conversation in a recent online course about the juxtaposition between the focus of...

read more## A Grade 5 Q&A: Percents

Question: Why was the work with percents taken out of the 5th grade curriculum in the 3rd edition? Answer: In the 1st and 2nd editions of Investigations, there was a unit (Name that Portion and What’s That Portion?) that included lessons that connected what 5th graders already knew about percents to what they already knew about fractions and decimals. These concepts were taught together, rather than separately, and built strong conceptual understandings of the meaning of percents and their...

read more## Helping with Math Homework

In schools that use Investigations, families often feel unsure of how to help their children with math homework. Many parents/caregivers have told me that they don’t understand the strategies their children are using and don’t know what to do if their child is struggling with a homework assignment. The math education field has work to do to help families make sense of how math is being taught, and to help them figure out how to support their children in mathematics learning. However, I think a...

read more## Multiplication in 5th Grade: What Are Some Issues?

Last year, my colleague Keith and I worked a few times with a group of 5th grade teachers. One of the questions they asked us to help them think about related to this 5th grade benchmark: “Fluently solve multidigit multiplication problems using a variety of strategies including the U.S. standard algorithm.” They told us that they had students who could multiply 2-digits by 2-digits successfully but struggled with 3-digit by 2-digit multiplication problems. They wanted to discuss the...

read more## A Grade 2 Q&A: The Size of the Numbers

Question: If the CCSS indicates that Grade 2 students are supposed to be working with numbers to 1,000, why doesn’t this work begin sooner? Why are students still working with numbers under 20 and numbers under 100 for so much of the year? Answer: The Common Core State Standards at Grade 2 include work with numbers up to 1,000, but it is important to look closely at what students are expected to do with these numbers. In Grade 2 students are developing efficient and accurate strategies...

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